In wireless sensor networks, sensor nodes located close to the base station or sink are more susceptible to energy loss, leading to premature disconnection of the network or energy holes. This is due to the fact that all traffic is forwarded towards the sink, increasing the workloads for these closer nodes. One solution for this issue is to shorten the hop distance a sensor’s data has to travel until reaching the sink, by deploying additional relay nodes. This paper considers the problem of optimal relay node placement for maximizing the network lifetime of wireless sensor networks in three-dimensional terrains. We first design a mathematical model of the problem and reformulate it as a mixed-integer programming model to provide a basis for finding lower bound solutions. We divide the problem into two phases and show that the second phase can be solved exactly using an algorithm based on maximum flow and binary search. We then propose a local search algorithm for the first phase, utilizing the exact algorithm to create full solutions. Experimental validation on 3D datasets has been carried out to demonstrate the performance of our algorithms.

在无线传感器网络中，靠近基站或接收器的传感器节点更容易遭受能量损失，从而导致网络或能量孔过早断开。这是由于以下事实：所有流量都转发到接收器，从而增加了这些较近节点的工作量。解决此问题的一种方法是，通过部署其他中继节点来缩短传感器数据在到达接收器之前必须经过的跳跃距离。本文考虑了最佳中继节点放置的问题，以最大化三维地形中无线传感器网络的网络寿命。我们首先设计问题的数学模型，并将其重新构造为混合整数编程模型，从而为寻找下界解提供基础。我们将该问题分为两个阶段，并表明可以使用基于最大流量和二进制搜索的算法来精确解决第二阶段。然后，我们为第一阶段提出一种本地搜索算法，利用精确算法创建完整的解决方案。已经对3D数据集进行了实验验证，以证明我们算法的性能。